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arXiv · 0805.3652

On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al

A. Pluchino·A. Rapisarda·C. Tsallis
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Abstract

In the present paper we refute the criticism advanced in a recent preprint by Figueiredo et al [1] about the possible application of the $q$-generalized Central Limit Theorem (CLT) to a paradigmatic long-range-interacting many-body classical Hamiltonian system, the so-called Hamiltonian Mean Field (HMF) model. We exhibit that, contrary to what is claimed by these authors and in accordance with our previous results, $q$-Gaussian-like curves are possible and real attractors for a certain class of initial conditions, namely the one which produces nontrivial longstanding quasi-stationary states before the arrival, only for finite size, to the thermal equilibrium.

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A. Pluchino, A. Rapisarda, C. Tsallis. 2009-03-14. On "Ergodicity and Central Limit Theorem in Systems with Long-Range Interactions" by Figueiredo et al. https://doi.org/10.1209/0295-5075%2F85%2F60006

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